Expert: Josh - 9/19/2005

Question
(5 – 9)2 ÷ 8 • 3 + 5    


HOW DO I GET THE ANSWER TO THIS?

Answer
Hi Jay,

Here are the order of precedance for the four basic operations.

1    Parentheses (),[], etc.
2    Multiplication (*) and Division (/)
3    Addition (+) and Subtraction (-).

Here are the rules:
1. Always do the multiplications and divisions, before additions and subtractions.
2. Work your way from left to right.
3. If you see any expression enclosed inside parentheses, evaluate these terms first.

Note: * and / are considered to be equally important, so if you encounter division before multiplication, like in 10/2*4, you do the division (10/2) first, before you multiply the result by 4. Ans: 10/2*4=5*4=20 On the other hand, if you see 10*2/4, you do the multiplication (10*2) first, before you divide the result by 4. Ans: 10*2/4=20/4=5)

Answer to your question:
(5 – 9)2 ÷ 8 • 3 + 5
step 1: simplify expression inside ( )
=(4)2 ÷ 8 • 3 + 5
= 4 * 2 ÷ 8 • 3 + 5
note: we can rewrite (4)2 as 4*2
step 2: first operator "*" is a multiplication, so multiply 4 by 2, we have
= 8 ÷ 8 • 3 + 5
step 3: going from left to right, the next operator is "/", so divide 8 by 8
= 1 • 3 + 5
step 4: going from left to right, the next operator is "*", so multiply 1 by 3
=3 + 5
=8

More examples:
eg.1 Simplify 2 - 4 / 2 * 3 - 1
2 - 4 / 2 * 3 - 1 ...remember, do division/multiplication first
=2 -(4 / 2)* 3 - 1
=2 - 2 * 3 - 1
=2 - (2 * 3) - 1
=2 - 6 - 1
=(2 - 6) - 1
=-4 -1
=-5

eg.2 Simplify 20 /(4 - 2) - 3 * 1
simplify expression inside parentheses first
20 /(4 - 2) - 3 * 1
=20/2-3*1
going from left to right, we first encounter a division, so do this first
=(20/2)-3*1
=10-3*1
going from left to right, we first encounter a subtraction first...but, multiplication has higher precedence compared to subtraction, so we multiply 3 by 1 first.
=10-(3*1)
=10-3
=7

Hope this is okay.